[KyleGoetz]

To simplify what RickOShay said, there are two types of verbs. Ichidan and godan.

Ichidan verbs are ones that drop る and add ます in polite non-past. 食べます、止めます, etc. Every ichidan ends with /eru/, but not every verb ending in /eru/ is ichidan.

Godan verbs are everything else except する／来る (the two verbs considered irregular most of the time). You can think of them as the ones that drop and add /imasu/ to the stem for polite non-past. 飲みます、作ります, etc.

For the potential form of ichidan verbs, drop る and add られる. For ichidan verbs, you change the stem's ending to /e/ and add る.

Examples:
ichidan
食べるー＞食べられる
止めるー＞止められる
godan
飲むー＞飲める
作るー＞作れる
irregular
するー＞できる
来るー＞来（こ）られる

I'd suggest reading Tae Kim's guide (or a textbook, really) to get a better explanation than we are willing to type here. It's not like it's an esoteric thing that isn't explained in every Japanese textbook on the planet.

And learn the terms "ichidan" and "godan." It will make it much easier to explain things in the future.